Reference no: EM132847915

Consider the following sample of observations on coating thickness for low-viscosity paint ("Achiev- ing a Target Value for a Manufacturing Process: A Case Study," J. Qual. Technol., 1992: 22-26):

.83 .88 .88 1.04 1.09 1.12 1.29 1.31 1.48 1.49 1.59 1.62 1.65 1.71 1.76 1.83

Assume that the distribution of coating thickness is normal (a normal probability plot strongly sup- ports this assumption).

-Calculate a point estimate of the mean value of coating thickness, and state which estimator you used.

-Calculate a point estimate of the median of the coating thickness distribution, and state which estimator you used.

-Calculate a point estimate of the value that separates the largest 10% of all values in the thickness distribution from the remaining 90%, and state which estimator you used. [Hint: Express what you are trying to estimate in terms of m and s]

-Estimate P(X < 1.5), i.e., the proportion of all thickness values less than 1.5. [Hint: If you knew the values of m and s, you could calculate this probability. These values are not available, but they can be estimated.]

-What is the estimated standard error of the estimator that you used in part (b)?

Answers in book (but I need worked out solutions to understand why these answers are correct):

-1.3481
-1.3481
-1.78
-0.97
-0.0846